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Multiple periodic-soliton solutions of the \((3+1)\)-dimensional generalised shallow water equation

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Abstract

Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of \((3\,{+}\,1)\)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.

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Acknowledgements

The authors acknowledge National Natural Science Foundation of China (Grant Nos 11571049 and 61370195) and Science and Technology project of Jiangxi Provincial Health and Family Planning Commission (20175537).

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Ye-Zhou Li & Jian-Guo Liu

  2. College of Computer, Jiangxi University of Traditional Chinese Medicine, Nanchang, 330004, Jiangxi, China

    Jian-Guo Liu

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  1. Ye-Zhou Li
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Correspondence to Jian-Guo Liu.

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Li, YZ., Liu, JG. Multiple periodic-soliton solutions of the \((3+1)\)-dimensional generalised shallow water equation. Pramana - J Phys 90, 71 (2018). https://doi.org/10.1007/s12043-018-1568-3

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  • DOI: https://doi.org/10.1007/s12043-018-1568-3

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